America's Red Rock Wilderness Act of 2013 - Designates specified lands in the following areas of Utah as components of the National Wilderness Preservation System: (1) Great Basin, (2) Grand Staircase-Escalante, (3) Moab-La Sal Canyons, (4) Henry Mountains, (5) Glen Canyon, (6) San Juan-Anasazi, (7) Canyonlands Basin, (8) San Rafael Swell, and (9) Book Cliffs and Uinta Basin.
Sets forth administrative provisions regarding: (1) the exchange of state-owned lands within such areas, (2) federal reservation of water rights, (3) measurement of setbacks for roads with wilderness, (4) authorized livestock grazing, and (5) withdrawal of such lands from disposition under certain public land laws.